Up all night? Caffeine crave may cause longterm health problems. Homework, jobs, and studying all may be causes for teens to consume too much coffee in their everyday lives. Health officials warn that high caffeine intake is not good for anyone, but coffee drinking continues to become more and more popular. It is not the coffee that is of concern; it is the amount of caffeine. A moderate amount of caffeine is nothing to worry about, health experts say. There are no health risks drinking three 8-oz cups of regular coffee, which is about 250 mg of caffeine each day, according to the Henry Ford Health System.

Source: New Expressions, http://www.newexpression.org/

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A nationwide random sample of college students revealed that 24 students consumed a total of 5428 mg of caffeine each day, with a standard deviation of 48 mg. Assuming that the amount of caffeine consumed per person daily is normally distributed, is there sufficient evidence to conclude that the mean amount of caffeine consumed daily by college students is less than 250 mg, using   0.05?

a. Complete the test using the p-value approach.

Include t, p-value, and your conclusion.

b. Complete the test using the classical approach.

Include the critical values, t, and your conclusion.